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Proof step 26 from proof mod-mult-law (previous step)

i = i |%| j + j * j0, i0 = i0 |%| j + j * j1, 0 < j ⊦ (i * i0) |%| j = (i * (i0 - j * j1)) |%| j, j = 0, i * i0 = i * (i0 - j * j1) + (j1 * i) * j

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i0, j * j1, i1] flags:

Additional information

Used simplifier rules: mod-mult-add: ⊦ 0 < j → (i + i0 * j) |%| j = i |%| j;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i0, j * j1, i1